Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings

DOI10.1007/978-3-319-38855-7_12zbMath1349.13045arXiv1510.02000OpenAlexW2261068068MaRDI QIDQ2826748

Bruce Olberding

Publication date: 18 October 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02000

zbMATH Keywords

Prüfer domainKrull domainvaluation ringspectral spaceZariski-Riemann spacePrüfer \(v\)-multiplication ring

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

Topological properties of localizations, flat overrings and sublocalizations, The Zariski-Riemann Space of Valuation Rings, Isolated points of the Zariski space, A principal ideal theorem for compact sets of rank one valuation rings, Ideal spaces: An extension of structure spaces of rings, Closure operations, continuous valuations on monoids and spectral spaces, The tree of quadratic transforms of a regular local ring of dimension two, Localizations of integer‐valued polynomials and of their Picard group, A connectedness theorem for spaces of valuation rings, On the topology of valuation-theoretic representations of integrally closed domains, Affine schemes and topological closures in the Zariski-Riemann space of valuation rings, Suprema in spectral spaces and the constructible closure, The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two, The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications, Topology, intersections and flat modules, When the Zariski space is a Noetherian space, Topological properties of subsets of the Zariski space

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